1. Field of the Invention
The present invention relates to a digital filter, and more specifically to improvement to a recursive digital filter to suppress noises in a no-signal condition.
2. Description of Related Art
In general, digital filters are composed of delay elements of one time slot delay or unit delay, multipliers for multiplication of constant values, and adders. The digital filter can be divided into a non-recursive filter and a recursive filter, and the latter is composed of a finite number of elements but is adapted to realize an infinite impulse response.
Referring to FIG. 1, there is shown one typical example of a conventional second-order recursive digital filter. The shown digital filter receives an input signal Xi and generates an output signal Yi, and includes a recursive digital filter loop composed two delay units D.sub.1 and D.sub.2, four multipliers M.sub.1, M.sub.2, M.sub.3 and M.sub.4, and four adders A.sub.2, A.sub.3, A.sub.4 and A.sub.5, coupled to one another as shown in FIG. 1.
The input signal Xi is supplied to a first input of the adder A.sub.2, which has an output connected to an input of the delay unit D.sub.1 and a first input of the adder A.sub.4. An output of the delay unit D.sub.1 is connected to respective inputs of the multipliers M.sub.1 and M.sub.3 and an input of another delay unit D.sub.2. The multiplier M.sub.1 multiplies the output of the delay unit D.sub.1 by a constant .beta..sub.1, and the multiplier M.sub.3 multiplies the output of the delay unit D.sub.1 by a constant .alpha..sub.1. An output of the delay unit D.sub.2 is connected to respective inputs of the multipliers M.sub.2 and M.sub.4. The multiplier M.sub.2 multiplies the output of the delay unit D.sub.2 by a constant .beta..sub.2, and the multiplier M.sub.4 multiplies the output of the delay unit D.sub.2 by a constant .alpha..sub.2. Outputs of the multipliers M.sub.1 and M.sub.2 are connected to two inputs of the adder A.sub.3, respectively, so that the outputs of the multipliers M.sub.1 and M.sub.2 are added to each other, and an output of the adder A.sub.3 is connected to a second input of the adder A.sub.2. Thus, the outputs of the multipliers M.sub.1 and M.sub.2 are added to the input signal Xi. Therefore, a feedback loop or recursive loop is formed. On the other hand, outputs of the multipliers M.sub.3 and M.sub.4 are connected to two inputs of the adder A.sub.5, respectively, and an output of the adder A.sub.5 is connected to a second input of the adder A.sub.4. An output of the adder A.sub.4 generates the output signal Yi.
The above mentioned digital filter will execute an operation for a differential equation expressed in the following: EQU Wi=Xi+.beta..sub.1 .multidot.W.sub.i-1 =.beta..sub.2.W.sub.i-2 EQU Yi=Wi+.alpha..sub.1 .multidot.W.sub.i-1 +.alpha..sub.2.W.sub.i-2
where i=. . . , -2, -1, 0,1,2, . . .
Xi=input signal PA1 Yi=output signal PA1 .alpha..sub.1, .alpha..sub.2, .beta..sub.1, .beta..sub.2 =constant PA1 Wi, W.sub.i-1, W.sub.i-2 =delayed data
As mentioned above, the conventional recursive digital filter is composed of delay units, multipliers and adders, each of which operates to execute a given operation in a finite length of word. Therefore, an error will inevitably occur due to rounding and truncation.
Thus, the error has been accumulated in the recursive digital filter loop of the conventional recursive digital filter, so that the result of operation will become non-linear. Particularly, when zero is inputted, a so-called limit cycle will occur in which the output will converge to a constant value which differs from zero, or the output value depicts a cyclic waveform. In other words, the output will not asymptotically approach to zero. This is a noise in a no-signal condition (no-signal noise), and this no-signal noise is a large problem in filtering a voice signal.
As means for preventing the occurrence of the limit cycle, it is considered to elongate the length of word in order to make small an error caused in rounding to a finite word length. This way requires a large amount of hardware, and therefore, is not preferably.